are one of the most ubiquitous sequences in mathematics. They have several combinatorial interpretations, some of which we include in Section REF . The comprehensive source for combinatorial interpretations of the Catalan numbers is [1]}, which lists no less than 214 interpretations of these numbers. Given some \(r \in \mathbb {N}\) , most of these combinatorial interpretations readily generalize to a sequence \((FC_{n}^{(r)})_{n \geqslant 0}\)  known as the Fuss-Catalan numbers. For example, [2]} defines these numbers by extending the notion of a Dyck path to a \(r\) -Dyck path.
